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Cosine Rule - Find an Angle

Cosine Rule - Find an Angle
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2012-12-05 07:59
TriangleTrigonometryGeometric Construction
This example demonstrates how to use the Cosine Rule to find an angle in a triangle. It involves core math concepts like the Cosine Rule. Construction uses GeoGebra commands/objects: Point, Circle, Intersect, Angle, Segment, Midpoint, If, Vector. Suitable for high school mathematics teaching and understanding practical applications of the Cosine Rule.

GeoGebra Commands & Parameters

  1. Point(Circle[R, c]) → Q
  2. Circle(Q, a) → d_1
  3. Circle(R, b) → c_1
  4. Intersect(c_1, d_1) → P, B_1, ,
  5. Angle(P, Q, R) → δ
  6. Angle(Q, R, P) → α_1
  7. Segment(P, R) → b_2
  8. Segment(R, Q) → c_2
  9. Segment(Q, P) → a_2
  10. Midpoint(a_2) → A'
  11. Midpoint(c_2) → C'
  12. Midpoint(b_2) → B'
  13. Midpoint(C', A') → D
  14. Midpoint(C', Q) → E
  15. Midpoint(A', Q) → F
  16. Midpoint(F, E) → G
  17. Midpoint(R, B') → H
  18. Midpoint(C', R) → I
  19. Midpoint(I, H) → J
  20. Midpoint(B', P) → K
  21. Midpoint(A', P) → L
  22. Midpoint(B', A') → M
  23. Midpoint(K, L) → N
  24. Midpoint(N, M) → O
  25. If(CosA < 0, "-", "") → signCosA
  26. If(CosB < 0, "-", "") → signCosB
  27. Segment(R, Q) → a_1
  28. Segment(R, P) → b_1
  29. Segment(P, Q) → e_1
  30. Angle(R, P, Q) → ε
  31. Vector(R, A') → u
  32. Vector(P, C') → w
  33. Vector(Q, B') → v

AI Drawing Prompt Reference

Draw a triangle with labeled sides and calculate an angle using the cosine rule. Start by drawing two intersecting circles to form the triangle. Mark the midpoints of each side and connect them. Represent the direction from vertices to midpoints with vectors. Finally, calculate and label the angle using the cosine rule, noting the sign.
The prompt above was compiled from the original drawing commands and is for reference only.